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2996
Ind. Eng. Chem. Res. 1997, 36, 2996-3001
Modeling CO Oxidation on Silica-Supported Iron Oxide under
Transient Conditions
Harvey Randall, Ralf Doepper, and Albert Renken*
Institute of Chemical Engineering, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland
The oxidation of CO on silica-supported hematite (Fe2O3) was studied by the step-response
method in a tubular fixed-bed reactor, at temperatures ranging between 270 and 350 °C. The
oxidation process appeared to proceed through two stages. Firstly, oxygen atoms adsorbed on
the surface of hematite react with gas phase CO according to an Eley-Rideal mechanism. Once
that adsorbed oxygen has been consumed to some extent, surface oxygen from the lattice of iron
oxide is removed in a second stage involving CO adsorption and CO reactive desorption steps,
thus generating surface oxygen vacancies. Further reduction of hematite proceeds through
diffusion of subsurface oxygen into surface oxygen vacancies. On this basis, a kinetic model
was developed, which quantitatively describes the transient behavior of the oxidation process.
The activation energies and pre-exponential factors of the rate constants and characteristic
subsurface oxygen diffusion time could be determined.
Introduction
The oxidation of CO is an important step during the
overall reduction of NO with CO on Fe2O3/SiO2. NO
and N2O reduction only occur on reduced catalysts
(Fe3O4), by reaction with surface oxygen vacancies. As
a result, the catalyst is reoxidized to hematite, which
is no longer active for reducing NO and N2O (Randall
et al., 1996a,b). The role of CO is to reduce the catalyst
in order to maintain a sufficient concentration of surface
oxygen vacancies for NO and N2O reduction to take
place. The aim of this work is to provide a quantitative
description of the reduction of Fe2O3/SiO2 by CO, which
could eventually be applied to the overall reduction of
NO or N2O by CO. As a matter of fact, the number of
kinetic parameters to be adjusted to experimental data
is considerably reduced by a study of the interaction of
CO with the catalyst independently.
In this work, the step-response methodswhich consists of measuring the response of a catalytic system to
a square like change in concentration of the reactantsswas chosen for its simplicity of application and
for the substantial amount of mechanistic information
that it provides (Kobayashi 1974, 1982; Bennett, 1976;
Tamaru, 1983; Kiperman, 1991; Renken, 1993). We
found it important to perform step changes in a wide
range of state variables such as temperature, flow rate,
and CO concentration, in order to obtain a meaningful
kinetic model with reliable values of its parameters.
Experimental Section
Transient experiments were carried out in a flow
apparatus consisting of two separate feed sections
converging to a four-way valve, which allowed generation of concentration step changes at the reactor inlet.
Both feeds contained pure gases (>99.99%, Carbagas,
Lausanne, Switzerland). The reactor used in this study
was a glass fixed-bed tubular reactor (internal diameter,
5 mm; length, 300 mm), which can be considered as a
plug flow reactor, as shown previously (Randall et al.,
1996b). The catalyst was Fe2O3/SiO2 (200 < dp < 250
µm) which was prepared by iron nitrate impregnation
and calcination (Randall et al., 1996a). For the experi* Author to whom correspondence should be addressed.
E-mail: [email protected].
S0888-5885(96)00613-6 CCC: $14.00
Figure 1. N2O and CO molar fraction at reactor inlet as a
function of time for catalyst pretreatment (oxidation with N2O)
and subsequent reduction with CO.
ments, 250 mg of catalyst was used. Gases at the
reactor outlet stream were analyzed with a quadrupole
mass spectrometer (QMG420, Balzers AG, Balzers,
Principality of Liechtenstein). Prior to transient experiments, the catalyst was oxidized in a flow of N2O (yN2O,0
) 0.004, Q ) 100 mL (NTP)/min, p ) 150 kPa) at 310
°C for 40 min, which assures total oxidation to Fe2O3
(Randall et al., 1996b). The N2O feed was then changed
to pure Ar, and the temperature of the catalyst was set
to the desired value. Transient experiments then
consisted in step changes of CO inlet mole fraction (from
0 to yCO,0), performed by the substitution of the Ar flow
with a mixture of CO and Ar (same pressure and flow
rate). The molar fractions of N2O and CO generated at
the reactor inlet respectively for catalyst oxidation and
catalyst reduction are depicted in Figure 1. These
transients were performed at different temperatures
(251 < T < 351 °C), inlet CO mole fractions (0.01 < yCO,0
< 0.03), and flow rates (50 < Q < 200 mL (NTP)/min).
All transients were found to be almost isothermal: the
temperature change during experiments never exceeded
1.5 °C. The slight deviation of the inlet function yCO,0
(t)swhich is generated at the reactor inlet after the inlet
flow was switched from pure Ar to CO/Arsfrom the
ideal square function was taken into account for modeling of the different experimental flow rates and CO feed
concentrations. Effect of internal diffusion of gaseous
© 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2997
Figure 2. Response to a CO concentration step on an oxidized
catalyst. Conditions: T ) 310 °C, yCO,0 ) 0.017, Q ) 100 mL (NTP)/
min.
CO is negligible, as previously shown by the comparison
of transient experiments with different particle sizes
(Randall et al., 1996c). Moreover, no external transport
limitations were encountered, since the rate of external
transport of gaseous CO was estimated to be 800 times
higher than the highest measured CO oxidation rate.
A more detailed description of the experimental setup
and procedures is given elsewhere (Randall et al.,
1996a).
Results and Discussion
Qualitative Interpretation of Transients. Figure
2 shows a typical transient response of the catalyst to
a concentration step of CO over an oxidized catalyst
(conditions: T ) 310 °C, yCO,0 ) 0.017, Q ) 100 mL
(NTP)/min). The response of CO2 shows an instantaneous maximum, followed by a second broader maximum. After a few hundred seconds, the reaction rate
falls to very low values, but CO2 is still observed for over
an hour. During the first hundred seconds of the
transient, the amount of converted CO (calculated by
subtracting the response of CO to the outlet function,
i.e. the response to a step wise increase in concentration
of an inert tracer with the same inlet concentration as
CO) is higher than the amount of CO2 formed, indicating
that a carbon-containing species is adsorbed on the
catalyst. Thereafter, the CO2 response becomes higher
than the response of converted CO, indicating that, in
this period, the rate of CO adsorption is lower than the
rate of CO2 formation. The carbon-balance defect was
observed for all experimental runs.
The appearance of two maxima in the CO2 responses
indicates that CO oxidation takes place in two stages.
The first step can certainly be described by an EleyRideal reaction between gas phase CO and surface
oxygen, since the first maximum is instantaneous. The
appearance of the second maximum can be explained
by the reaction of CO at another type of surface sites,
which are not present in a sufficient amount at the
beginning of the experiment and which are produced
during the first Eley-Rideal step. Furthermore, the
carbon-balance defect encountered during the transients
implies that the second reduction process of the catalyst
must include a carbon-containing surface species. Finally, the tailing of the CO and CO2 responses is
presumably due to the limitation of the reduction of the
catalyst by subsurface oxygen diffusion, as was observed
for the oxidation of the catalyst by N2O and NO (Randall
et al., 1996a,b). Upon oxidation of magnetite with
subsequent pulses of N2O and Ar (Randall, 1996c), it
was shown that, after a period under Ar, the rate of
oxidation of the catalyst by N2O is higher than the rate
at the end of the previous period under N2O. This
phenomena was shown to occur through diffusion of
oxygen abstracted from N2O at the surface of the
catalyst into subsurface oxygen vacancies. As a result,
the concentration of surface oxygen vacancies increases
during the period under Ar, and consequently the rate
of oxidation of the surface upon recontacting the catalyst
with N2O is higher than the rate at the end of the
previous period under N2O. This behavior cannot be
described by a simple shrinking core model, for which
there is no effect on the rate of oxidation of the catalyst
when it contacts an inert gas, since there is no possible
equilibration of the concentrations of solid species
(lattice oxygen and lattice oxygen vacancies) during this
period. Furthermore, the shrinking core model consists
of a reaction zone moving toward the center of the
particle whereas, in our case, the reaction between N2O
and surface oxygen vacancies only takes place at the
outer surface of the solid, since N2O has no access into
the bulk of the catalyst.
By investigating the formation of adsorbed oxygen on
Fe2O3 and NiO by temperature-programmed desorption,
Iwamoto et al. (1976, 1978a,b) have demonstrated the
existence of at least four states of adsorbed oxygen, the
maxima of which appeared at 50-300 (R), 350-360 (β),
480-490 (γ), and >600 °C (δ), respectively. γ and δ
oxygen were assigned to O- species adsorbed on different surface sites. Furthermore, by measuring the
change in electrical conductivity of Fe2O3 in NO and
N2O atmospheres, Sazonova et al. (1977) showed that
negatively charged particles are formed, which they
assigned to adsorbed O- or adsorbed N2O- species.
Evidence for the existence of adsorbed oxygen atoms
(O-) on NiO was also found by determination of the
mean electric charges acquired by an oxygen atom on a
NiO surface (Bieranski and Najbar, 1972), or by means
of XPS (Robert et al., 1972). Similarly, Alkhazov et al.
(1976) have reported the formation of adsorbed oxygen
on Cr2O3, which they call excess oxygen. Sokolovskii
(1990), proposed a generalized scheme that applies for
oxidative catalysis on solid oxides. He suggests a twostep oxygen activation process, by which a primary
activated form of surface oxygen (radical ion form such
as O- or O2-) is first formed, which subsequently
transforms into less active oxygen of the catalyst lattice.
Dekker (1995) found that reduction of alumina-supported copper oxide proceeds according to a two-step
mechanism, involving two different types of surface
oxygen: the first type reacts via an Eley-Rideal mechanism, whereas the second type reacts via a LangmuirHinshelwood mechanism.
In a previous study (Randall, 1996c), it was shown
that the amount of oxygen that can be transferred to
the catalyst (oxygen capacity) is 16% higher than the
amount of oxygen corresponding to the transformation
of Fe2O3 to Fe3O4 by performing successive reductionoxidation cycles of Fe2O3 to Fe3O4 with CO and N2O,
respectively. This observation is consistent with the
formation of adsorbed oxygen on Fe2O3 during treatment with N2O.
On the basis of the qualitative analysis of the transient responses of oxidized catalysts to concentration
steps of CO combined to the information from literature
cited above, the following three-step mechanism is
proposed for CO oxidation (eqs 1, 2, and 3). In eqs 1, 2,
and 3, O(O) represents an oxygen atom adsorbed on an
oxidized site from the surface of iron oxide, (O) stands
2998 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
ker
CO + O(O) 98 CO2 + (O)
kad
CO + (O) 98 CO(O)
(1)
(2)
kd
CO(O) 98 CO2 + ( )
(3)
for surface oxygen from the iron oxide lattice, and ( )
symbolizes a surface oxygen vacancy. For a CO concentration step on an oxidized catalyst, the first step
(eq 1) leads to an immediate production of CO2 (first
maximum). CO adsorption (eq 2) takes place only once
the adsorbed oxygen (O(O)) has been consumed to some
extent, and finally the reactive desorption of adsorbed
CO (eq 3) leads to a secondary formation of CO2 (second
maximum). Further reduction of the catalyst proceeds
through diffusion of subsurface lattice oxygen into
surface oxygen vacancies. The surface reaction and the
subsurface diffusion processes are schematically described in Figure 3.
Model Equations. Rate Equations. The kinetics of
the three steps of CO oxidation (eqs 1, 2, and 3) were
described using the following rate equations:
rer ) kercCOθOO
(4)
rad ) kadcCOθO
(5)
rd ) kdθCO
(6)
The surface coverages are defined as
θk ) ck/Ns
(7)
Ns, the total amount of sites, was taken as the amount
of oxygen corresponding to the transformation of Fe2O3
to Fe3O4. A value of Ns ) 0.33 mol/kgcat was obtained
(Randall, 1996c).
Mass Balance for Gas Phase Species in a Nonstationary Tubular Plug Flow Reactor. The mass
balance equation for a gas phase species j (CO or CO2)
is given by the expression
1 - b
∂cj
1 ∂cj
)+ RjFcat
∂t
τ ∂x
b
(8)
Variables and parameters are defined in the Nomenclature section.
τ in eq 8 is the space-time referred to gas volume.
The rate Rj in eq 8 is given by
RCO ) -rer - rad
(9)
RCO2 ) rer + rd
(10)
For a CO concentration step from 0 to yCO,0 at t ) 0, the
initial condition for gas phase species (CO or CO2) is
cj(x,0) ) 0
(11)
and the boundary conditions at the reactor inlet (x ) 0)
are given by
cCO(0,t) ) (p/RT)yCO,0(t)
cCO2(0,t) ) 0
}
(12)
Mass Balance for Surface Species. For adsorbed
oxygen and adsorbed CO species, the following mass
balance equations apply:
Figure 3. Schematic representation of the reduction of an iron
oxide crystallite by CO: (a) Eley-Rideal reaction, (b) CO adsorption, (c) CO reactive desorption, (d) subsurface oxygen diffusion.
td ) characteristic diffusion time.
(∂θOO/∂t) ) (-rer/Ns)
(13)
(∂θCO/∂t) ) ((rad - rd)/Ns)
(14)
The dimensionless concentration of lattice oxygen, θO,
is a function of x, z, and t, where z is the distance into
the iron oxide layer.
For spherical iron oxide crystallites, the dimensionless
mass balance equation for θO at the surface (z ) 1,
where θO ) θO,s) is
(
)
2
∂θO,s
∂θO
1 ∂ θO
(x,z ) 1,t) )
+2
2
∂t
td ∂z
∂z
z)1
+
rer - rad
(15)
Ns
where td is the characteristic diffusion time of oxygen
into the iron oxide layer.
In the bulk of the iron oxide layer (z < 1), where no
reaction occurs
(
)
2
∂θO
1 ∂ θO 2 ∂θO
(x,z < 1,t) )
+
∂t
td ∂z2
z ∂z
(16)
For a totally oxidized catalyst, the initial conditions for
eqs 13, 14, 15, and 16 are the following (the hypothesis
was made that the surface is initially totally covered
with adsorbed oxygen O(O)):
θOO(x,0) ) 1
(17)
θCO(x,0) ) 0
(18)
θO(x,z < 1,0) ) 1
(19)
θO(x,z ) 1,0) ) 0
(20)
The iron oxide crystallites on the surface of the silica
support can be considered to be symmetrical around
their centerplanes. Therefore, the boundary condition
at the center (z ) 0) of the particle is
∂θO
(x,0,t) ) 0
∂z
(21)
The system of partial differential equations in eqs 8,
13, 14, 15, and 16 was solved using the finite difference
approximation method (Simusolv, 1990; Crank 1957),
using nine nodes in the x direction and 40 nodes in the
z direction; these are the minimum number of nodes
above which the calculated responses did not change
any further. Numerical integration was carried out
using a variable step algorithm (Gear) (Simusolv, 1990).
Optimization of parameters td, ker, kad, and kd was
performed by fitting the calculated molar fractions of
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 2999
Figure 4. Comparison between model and experiment for a CO
concentration step on an oxidized catalyst at different temperatures. Conditions: yCO,0 ) 0.017, Q ) 100 mL (NTP)/min. (a) CO
response, (b) CO2 response.
CO and CO2 at the outlet of the reactor to their
experimental values, using the Nelder-Mead search
algorithm and the likelihood function as the objective
function (Simusolv, 1990). Initial estimates for parameters ker and td, which essentially affect the first peak
in the CO2 response and the tailing in the CO2 response,
respectively, were readily obtained. In order to obtain
two maxima in the CO2 response, it was found that
parameters kad and kd have to be of the same order of
magnitude. Finally, the optimum values of parameters
were determined by simultaneous optimization of all
parameters using different sets of initial estimates for
kad and kd.
Parameter Estimation. In Figures 4 and 5, the
experimental transient responses at various temperatures and inlet CO mole fractions are compared to the
calculated responses with optimum values of parameters td, ker, kad, and kd. As can be seen from these
figures, the three-step oxidation model of eqs 1, 2, and
3, combined with subsurface diffusion of lattice oxygen,
allows us to predict the transient reduction of the
catalyst over a wide range of the dependent variables
T and yCO,0. Similar fittings were obtained at other flow
rates. The model is able to describe the increase in the
ratio of the intensities of the second maximum to the
first maximum with temperature as well as the shift of
the second maximum to shorter times with increasing
temperature. The shift of the second maximum to
shorter times with increasing CO inlet molar fraction
is also properly described. However, a divergence
between model and experiment is observed at high
reaction times (t > 200-300 s), which may be due to
the fact that subsurface diffusion was modeled in
spherical coordinates, whereas the structure of iron
Figure 5. Comparison between model and experiment for a CO
concentration step on an oxidized catalyst at different inlet CO
molar fractions. Conditions: T ) 310 °C, Q ) 100 mL (NTP)/min.
(a) CO response, (b) CO2 response.
Figure 6. Calculated responses of catalyst surface species at
different positions x in the reactor for a CO concentration step on
an oxidized catalyst. Conditions: T ) 310 °C, yCO,0 ) 0.017, Q )
100 mL (NTP)/min.
oxide crystallites may differ significantly from the ideal
spherical geometry.
Figure 6 gives the calculated spatiotemporal behavior
of catalyst surface species (at z ) 1) with optimum
values of parameters, at T ) 310 °C, yCO,0 ) 0.017, and
Q ) 100 mL (NTP)/min. θOO decreases relatively fast
due to the Eley-Rideal reaction between adsorbed
oxygen and gas phase CO. As a result, θO at the surface
rises and, subsequently, goes through a maximum at
approximately 70 s due to CO adsorption on surface
lattice oxygen. At the beginning of the transient, CO
adsorption is faster than CO reactive desorption, leading
3000 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997
Table 1. Activation Energies and Pre-exponential Factors
104ker0
[m3/kgcat‚s]
104kad0
[m3/kgcat‚s]
105kd0
[mol/kgcat‚s]
103(1/td0)
[s-1]
Eer
[kJ/mol]
Ead
[kJ/mol]
Ed
[kJ/mol]
Ediff
[kJ/mol]
1.3 ( 0.6
1.1 ( 0.4
2.7 ( 1.6
1.4 ( 1.6
75 ( 2
73 ( 2
88 ( 3
69 ( 7
Figure 7. Calculated gas phase responses for a CO concentration
step on an oxidized catalyst. Conditions: T ) 310 °C, yCO,0 ) 0.017,
Q ) 100 mL (NTP)/min.
Figure 9. Arrhenius plot for the rate constants (ker, kad, and kd)
and the reverse characteristic diffusion time (1/td).
The optimum values of parameters 1/td, ker, kad, and
kd obtained for all runs were used to determine the
activation energies and pre-exponential factors of the
corresponding reaction or diffusion processes (Table 1).
All parameters could be fitted with the Arrhenius law,
as shown in Figure 9, where the natural logarithms of
their values are plotted versus reverse temperature (for
T ) 310 °C, the average values of parameters obtained
for the different runs performed at this temperature are
plotted). The value obtained in the present work for
Ediff (69 ( 7 kJ/mol) during reduction of hematite is close
to the values obtained by Castle and Surmann (1969)
(71 kJ/mol) and Heizmann et al. (1973) (109 kJ/mol) for
oxygen diffusion in Fe3O4 or Gillot (1981) for diffusion
of iron ions in hematite (89.9 kJ/mol).
Figure 8. Calculated spatiotemporal behavior of catalyst surface
and bulk lattice oxygen at x ) 0.5 (middle of reactor) for a CO
concentration step on an oxidized catalyst. Conditions: T ) 310
°C, yCO,0 ) 0.017, Q ) 100 mL (NTP)/min.
to an accumulation of adsorbed CO. As a result, the
amount of converted CO exceeds the CO2 response
(Figure 7). After 70 s, the diminution of θO at the
surface causes a faster rate for CO reactive desorption
than for CO adsorption. Consequently, the amount of
converted CO becomes lower than the that from the CO2
response. Accordingly, the maximum in θO at the
reactor outlet and for z ) 1 (surface) arises at the same
time (approximately 70 s) as the crossing between CO2
and converted CO responses.
Thus, the model accounts for the complex relation
between the responses of CO2 and adsorbed CO encountered experimentally (Figure 2). The decrease in θCO
and θO at the surface after 70 s is relatively slow, since
lattice oxygen is slowly transferred to the surface by
diffusion from the bulk of the iron oxide. This last point
is depicted in Figure 8, where θO in the middle of the
reactor (x ) 0.5) at different positions in the catalyst
(z) is plotted versus time. The resistance to oxygen
transfer in the catalyst gives rise to a gradient of θO as
a function of z. Due to this resistance, the beginning of
the diminution in θO is increasingly delayed when it
approaches the center of the particle (i.e. with decreasing values of z).
Conclusions
A model was developed which quantitatively describes
the reduction of hematite by CO under transient conditions within a wide range of the state variables (temperature, CO concentration, and flow rate). The model
consists of three surface reaction steps as well as
subsurface oxygen diffusion. It accounts for the complex
features of the transient behavior of gas phase species
(CO and CO2) such as a carbon-balance defect, a twostage reduction process, and a long tailing in the
transient responses. The rate constants and the diffusion coefficient of oxygen in the iron oxide follow the
Arrhenius law.
Acknowledgment
We are grateful for financial support of this project
by the Swiss National Science Foundation.
Nomenclature
cCO ) gas phase concentration of CO, mol/m3
cCO2 ) gas phase concentration of CO2, mol/m3
cCO,0 (t) ) CO inlet concentration step function, mol/m3
c( ) ) oxygen vacancy concentration in the catalyst, mol/
kgcat
c(O) ) lattice oxygen concentration in the catalyst, mol/kgcat
cO(O) ) Concentration of adsorbed oxygen, mol/kgcat
cCO(O) ) concentration of adsorbed CO, mol/kgcat
Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3001
dp ) diameter of particles, m
Ei ) activation energy for process i, kJ/mol
ki ) rate constant for reaction step i, various units
ki0 ) pre-exponential factor, various units
Ns ) total concentration of sites ) 0.33 mol/kgcat
NTP ) normal conditions of temperature and pressure (0
°C, 1.013 × 105 Pa)
p ) pressure in the reactor, kPa
Q ) total volumetric flow rate, mL (NTP)/min
rad ) rate of CO adsorption step (eq 2), mol/kgcat‚s
rer ) rate of Eley-Rideal step (eq 1), mol/kgcat‚s
rd ) rate of CO reactive desorption step (eq 3), mol/kgcat‚s
RCO2 ) CO2 rate of formation, mol/kgcat‚s
RCO ) CO rate of disappearance, mol/kgcat‚s
Rj ) rate of transformation of gas phase species j, mol/
kgcat‚s
R ) gas constant, kJ/mol‚K
t ) time, s
td ) characteristic diffusion time, s
td0 ) characteristic diffusion time at infinite temperature,
s
T ) temperature, K
x′ ) distance from the reactor inlet, m
x ) dimensionless distance from the reactor inlet ()x′/L)
y ) molar fraction
yCO ) CO molar fraction
yCO2 ) CO2 molar fraction
yCO,0 ) CO molar fraction in feed
yCO,0 (t) ) CO inlet step function
yN2O,0 ) N2O molar fraction in feed
z′ ) distance from the center of the spherical geometry iron
oxide crystallite, m
z ) dimensionless distance from the center of the spherical
geometry iron oxide crystallite (z′/δ)
( ) ) lattice oxygen vacancy
(O) ) lattice oxygen
O(O) ) adsorbed oxygen species
CO(O) ) adsorbed CO species
Greek Letters
b ) void fraction of catalyst ) 0.5
φ ) degree of reduction of the catalyst
θO ) lattice oxygen coverage
θOO ) adsorbed oxygen coverage
θCO ) CO coverage
Fcat ) catalyst bulk density ) 373.5 kg/m3
τ ) space time referred to gas volume, s
Subscripts
0 ) inlet
ad ) subscript for CO adsorption step (eq 2)
er ) subscript for Eley-Rideal step (eq 1)
d ) subscript for CO reactive desorption step (eq 3)
diff ) subscript for subsurface oxygen diffusion process
i ) subscript for reaction or diffusion process (i ) ad, er,
d, or diff)
j ) index for gas phase species (CO, CO2, N2O)
k ) index for surface species ((O), O(O),(CO))
s ) index for the surface
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Received for review October 2, 1996
Revised manuscript received February 3, 1997
Accepted February 4, 1997X
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IE960613D
Abstract published in Advance ACS Abstracts, June 15,
1997.
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